Add MA1511 Recap

Author: mendax1234

24-S1/MA1511/README.md

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+# MA1511 Course Review
+## Introduction
+- **Full name**: [MA1511 Engineering Calculus](https://nusmods.com/courses/MA1511/engineering-calculus)
+- **Target audience**: NUS Year 1 Engineering Students
+- **Purpose of the course**: Foundational calculus knowledge preparing for modeling real-world system
+- **Notes Structure**:  
+   - **MA1511-Notes**: This folder contains a comprehensive version of my notes, designed to break down and explain each concept covered in the course in a clear and easy-to-understand manner.  
+   - **MA1511-Cheatsheet**: Here, you'll find the cheatsheet I created and used throughout the course, summarizing key formulas and methods for quick reference.  
+
+I took this course in AY24/25 Sem 1 for my degree requirement.
+
+## Course Content
+### Overview of Topics Covered
+1. **Partial Derivatives**: Level Curves, First Order Partial Derivatives, Higher Order Partial Derivatives, Normal Lines and Tangent Planes, Chain Rule, Directional Derivatives, Local Extrema, Lagrange Multipliers
+2. **Multiple Integrals**: Double Integrals over Rectangular Domain and General Domain, Double Integrals in Polar Coordinates
+3. **Vector Valued Functions**: Curves and Motion in Space, Integrals of Vector-valued Functions, Arc Length, Line Integrals, Parametric Surfaces
+4. **Vector Fields**: Vector Fields, Line Integrals of Vector Fields, Conservative Fields, Line Integrals in Conservative Fields, Green's Theorem, Curl and Divergence
+5. **Infinite Series**: Sequences, Infinite Series, Two Convergence Tests for Infinite Series, Power Series, Taylor Series, Maclaurin Series
+
+### Depth and Balance of Coverage
+
+- **Theoretical Understanding**:  
+   As an engineering mathematics course, the focus is primarily on applying equations to solve problems. However, I believe engineers should also develop a deeper understanding of the underlying concepts. This theoretical foundation will help in analyzing and solving real-world problems more effectively, beyond just computation.
+
+- **Application and Real-World Examples**:  
+   While this course touches on the geometric interpretation and representation of concepts, I feel like it falls short of incorporating practical real-world examples. This limitation might stem from the course's brief duration. From my point of view, incorporating at least a few detailed real-world applications would greatly enhance the learning experience.
+
+- **Challenging or Unique Aspects**:  
+   The most challenging aspect of this course, in my opinion, is developing **spatial imagination**. Understanding certain concepts through their geometric interpretations can make them significantly easier to grasp. Without this visualization, however, the material can become quite difficult to comprehend.
+
+## Teaching Style and Materials
+- **Lecture**:  
+   The lectures are conducted by Prof. Tan Ban Pin. The lecture notes are clear, concise, and easy to understand, making them an excellent resource for both learning during the semester and reviewing before the final examination.  
+
+- **Tutorial**:  
+   My tutorials are led by Clifton, who is an excellent instructor. He explains concepts clearly and is always approachable. The tutorial questions for this module are generally straightforward and not too challenging.
+
+- **Assessment**:  
+   The final examination is the primary assessment for this course. In my opinion, it is quite straightforward and mainly tests your familiarity with the formulas covered in the course. Most of the time, solving the problems involves directly substituting numbers into the equations, making it more of a test of accuracy than deep conceptual understanding.  
+
+
+## Learning Experience
+- **Personal Insights**:  
+   The workload for this course is relatively light, so if your goal is simply to pass or secure a good grade, you don't need to invest an excessive amount of time. However, if you aim to gain a deeper understanding of the concepts by reading the textbook, be prepared for it to be quite time-consuming. I noticed that the content of one week's lecture typically corresponds to an entire chapter in the textbook. That said, this course provides a valuable opportunity to revisit and deepen your understanding during the holidays.
+
+- **Skills Developed**:  
+   The calculus skills I developed in this course, including both integration and differentiation, are fundamental and incredibly important for succeeding in the follow-up module, MA1512 *Differential Equations for Engineers*.  
+
+## Workload and Time Management  
+- **Level of Difficulty**:  **4/10**
+- **Tips for Future Students**:  
+    I hope my notes will ease your workload and provide clarity on the concepts covered in this course. They are designed to help you grasp the material more effectively and approach the challenges with confidence.
+
+## Conclusion
+Calculus is a fundamental skill, especially for engineers. As for this course, I legit have no comment. However, one key takeaway is the importance of self-study, which is an essential skill to develop and rely on during university.

24-S1/MA1512/README.md

@@ -2,7 +2,7 @@
 ## Introduction
 - **Full name**: [MA1512 Differential Equations for Engineering](https://nusmods.com/courses/MA1512/differential-equations-for-engineering)
 - **Target audience**: NUS Year 1 Engineering Students
-- **Purpose of the course**: Foundational math for modeling real-world system
+- **Purpose of the course**: Foundational differential equations knowledge for modeling real-world system
 - **Notes Structure**:  
    - **MA1512-Notes**: This folder contains a comprehensive version of my notes, designed to break down and explain each concept covered in the course in a clear and easy-to-understand manner.  
    - **MA1512-Cheatsheet**: Here, you'll find the cheatsheet I created and used throughout the course, summarizing key formulas and methods for quick reference.  
@@ -50,24 +50,24 @@ I took this course in AY24/25 Sem 1 for my degree requirement.
 
 ### Depth and Balance of Coverage
 - **Theoretical Understanding**:  
-As a mathematics course designed for NUS Engineering freshmen, the focus is less on rigorous mathematical proofs and more on practical applications of theorems and techniques. However, the professor thoughtfully provides supplementary materials for those interested in exploring the derivations and deeper theoretical foundations.
+    As a mathematics course designed for NUS Engineering freshmen, the focus is less on rigorous mathematical proofs and more on practical applications of theorems and techniques. However, the professor thoughtfully provides supplementary materials for those interested in exploring the derivations and deeper theoretical foundations.
 - **Application and real-world examples**:  
-This course incorporates a moderate number of applications and real-world examples, many of which are interdisciplinary. For instance, it explores the harmonic oscillator (from Physics) and population dynamics (from Economics). These examples provide valuable insights, opening up a new perspective on how mathematics can be applied to explain and understand various phenomena!
+    This course incorporates a moderate number of applications and real-world examples, many of which are interdisciplinary. For instance, it explores the harmonic oscillator (from Physics) and population dynamics (from Economics). These examples provide valuable insights, opening up a new perspective on how mathematics can be applied to explain and understand various phenomena!
 - **Challenging or Unique Aspects**:
     1. **Formulating the Correct Differential Equation**:  
-    This is perhaps the most challenging aspect, as it often requires a strong understanding of interdisciplinary concepts, including principles from physics or other fields. Successfully crafting an accurate differential equation cultivates the ability to approach real-world problems systematically and step-by-step.  
+        This is perhaps the most challenging aspect, as it often requires a strong understanding of interdisciplinary concepts, including principles from physics or other fields. Successfully crafting an accurate differential equation cultivates the ability to approach real-world problems systematically and step-by-step.  
     2. **Solving the Differential Equation**:  
-    Once the equation is established, determining the appropriate method to solve it can be equally demanding. We’ve learned a variety of techniques, but choosing the right one depends on correctly identifying the type of differential equation at hand.  
+        Once the equation is established, determining the appropriate method to solve it can be equally demanding. We’ve learned a variety of techniques, but choosing the right one depends on correctly identifying the type of differential equation at hand.  
     3. **Strong Calculus Foundation**:  
-    A solid grasp of calculus is fundamental to solving differential equations. Proficiency in key concepts, such as differentiation and integration theorems, is essential for solving the differential equations.
+        A solid grasp of calculus is fundamental to solving differential equations. Proficiency in key concepts, such as differentiation and integration theorems, is essential for solving the differential equations.
 
 ## Teaching Style and Materials
 - **Lecture**:  
-The lectures are conducted by Prof. Christian, whose teaching is exceptional. He is, without a doubt, one of the best professors I’ve encountered at NUS! The lecture notes are well-structured, clear, and easy to follow. However, the lecture quizzes can occasionally be a bit tricky, adding an extra layer of challenge.  
+    The lectures are conducted by Prof. Christian, whose teaching is exceptional. He is, without a doubt, one of the best professors I’ve encountered at NUS! The lecture notes are well-structured, clear, and easy to follow. However, the lecture quizzes can occasionally be a bit tricky, adding an extra layer of challenge.  
 - **Tutorial**:  
-My tutorials are led by Clifton, who is both kind and exceptionally knowledgeable. The tutorial materials are well-designed and easy to understand, making complex concepts more approachable. While the tutorial assignments can be challenging and time-consuming, they are highly effective in helping us apply the theories we’ve learned to real-world scenarios.  
+    My tutorials are led by Clifton, who is both kind and exceptionally knowledgeable. The tutorial materials are well-designed and easy to understand, making complex concepts more approachable. While the tutorial assignments can be challenging and time-consuming, they are highly effective in helping us apply the theories we’ve learned to real-world scenarios.  
 - **Assessment**:  
-The assessment structure consists of 40% Continuous Assessment (CA) and 60% Final Exam. The final exam is the most challenging yet rewarding part of the course. This semester’s (AY24/25 Sem 1) paper was particularly well-designed, pushing us to think comprehensively and quickly, even though completing all the questions within the time limit was tough.
+    The assessment structure consists of 40% Continuous Assessment (CA) and 60% Final Exam. The final exam is the most challenging yet rewarding part of the course. This semester’s (AY24/25 Sem 1) paper was particularly well-designed, pushing us to think comprehensively and quickly, even though completing all the questions within the time limit was tough.
 
 ## Learning Experience
 - **Personal Insights**:  
@@ -80,7 +80,7 @@ The assessment structure consists of 40% Continuous Assessment (CA) and 60% Fina
    - **6/10**: If your goal is simply to pass the course.  
    - **9/10**: If you aim to excel and achieve a deep understanding of the material, beyond just the grades.  
 - **Tips for Future Students**:  
-   I hope my notes will ease your workload and provide clarity on the concepts covered in this course. They are designed to help you grasp the material more effectively and approach the challenges with confidence.
+    I hope my notes will ease your workload and provide clarity on the concepts covered in this course. They are designed to help you grasp the material more effectively and approach the challenges with confidence.
 
 ## Conclusion
 I would say that differential equations are one of the most essential tools for any engineer. They serve as a critical bridge between the worlds of mathematics and physics, enabling us to model and analyze complex systems. Many future physics-based analyses will rely heavily on this technique. I hope you find this course both meaningful and engaging!